At first all we see is a pale blob, but as we approach it resolves into a bundle of thick white fur – a week-old seal pup. Black-eyed and sleepy-looking, it lolls on the tussocky sand of north Lincolnshire’s Donna Nook nature reserve a few metres from its mother, who appears to be doing her best to ignore it.

“She’s just given it a good feed and she’s having a break,” says Peter, one of the volunteer wardens who patrol the reserve year-round, but especially at pupping time.

Peter tells us how the pups weigh 15kg at birth, and are a roly-poly 60kg by the time they’re weaned three weeks later, thanks to some of nature’s richest milk: it’s up to 60% fat and has the consistency of toothpaste. We also learn that seal mothers don’t get to feed between hauling themselves ashore to give birth and returning to the sea almost a month later. Their bellies are apparently quite concave by this point – and they’re already pregnant again.

We’re lucky to see an early pup in October half-term, but by December this windswept stretch of coast offers probably the country’s best wildlife experience. By mid-December, 2,024 pups had been born at Donna Nook, and while our little blob is some 10 metres from the path, space is at a premium later in the season, with seals giving birth, and mating, right by the fence – giving younger visitors a swift and graphic lesson in reproduction.

Human visitors to this coast come mostly in summer, when Europe’s biggest concentration of caravan parks is filled with families. But I think the Lincolnshire coast is at its magical best in winter. With average winter rainfall less than half that of, say, Devon, it can be a wonderland of big skies and crisp, clear light. Yes, north-easterlies from the coldest parts of Europe can barrel across the North Sea – but that’s what gloves and hats are for, and what makes cosy pubs like the thatched Kings Head at Theddlethorpe so appealing. And though days are short, the low-lying land means even in late afternoon the westering sun casts long rays over wide sandy beaches.

On one such afternoon we take a peek at the geometric shapes and big windows of the new North Sea Observatory at Chapel St Leonards (open in late 2018), then set off to walk the three miles back to our lodgings in Anderby Creek. Acres of scrub to our left glow with orange sea buckthorn. The sun picks out a lone fisherman on the beach (hoping for haddock or whiting, he tells us; sea bass if he’s lucky) and glints on the white blades of 70-odd offshore wind turbines. Peace, light and space (plus clean energy): what better antidote to city life?

Coastal chic .... the sitting area at Seaside Lodge Photograph: A Winfield

Our weekend hideaway is Seaside Lodge, a two-bedroom chalet minutes from the beach and overlooking a fishing lake, where geese honk and acrobatic starlings perform huge murmurations. Inside it is cosy and calm, with cream floorboards and seasidey blue-and white furnishing. It has been cleverly updated, with well-equipped kitchen, tiny en suite with rain shower, another bathroom and a wood-burning stove by the picture window. A welcome basket includes a loaf of Lincolnshire plum bread.

There’s more great walking next day, at Gibraltar Point nature reserve, south of Skegness, with six miles of footpaths over salt marsh, dunes, grassland and beach. Like Donna Nook, it is popular all year round with winged visitors; rare little terns spend summers here after wintering in Africa, and in winter it’s home to, among others, brent geese – smaller and prettier than your usual Canada goose. They come for the balmy weather: these shores are positively tropical compared with their Arctic breeding sites.

The reserve’s recently built visitor centre has glass walls on three sides, big views, good coffee, homemade cakes and interesting lunches, such as a butternut, goat cheese and beet burger. In really “fowl” weather it would be a congenial space to spend an hour or two, watching wheeling birds and the changing light over the dunes and wooded ridges.

There is plenty more to fill a long weekend or short winter break here: Skegness and Mablethorpe both have an out-of-season charm, and Theddlethorpe has a vast beach, almost a mile wide at low tide. We visit nearby five-mile-long Saltfleetby Theddlethorpe Dunes nature reserve – protected from the wind by a ridge – for an hour’s happy tramping among low, grassy hills bright with orange, red and black berries. We see tank traps, and take in beach views from several second world war concrete bunkers. We don’t see any natterjack toads, but this is apparently one of their few remaining habitats.

One rather oversold attraction is the (free) cloud-viewing platform at Anderby Creek, with information about cloud types, and angled mirrors for inspecting them. Sadly in Britain, even on its drier east coast, we know only too well what clouds look like.

The county’s gastronomic attractions, however, are very much undersold. The UK’s biggest fish market is just up this coast at Grimsby (Billingsgate, London, is the largest inland fish market) and no self-respecting restaurateur in these parts would get supplies from anywhere else.

Good fish is not a “regional speciality” around here; it’s just dinner – for seals and people. A plaice fillet (£10.50) at restaurant La Piazza in Chapel St Leonards comes with a Sicilian-tasting cherry tomato dressing, but the sweet, fine-textured flesh is the North Sea on a plate. It’s bettered only by battered haddock (£9.95) in the restaurant of the Grange and Links, a low-key hotel in a large garden close to Sandilands beach: fat chips made from dense Lincolnshire spuds accompany tender flakes of dreamy fish.

We may only have been taking brisk walks in brisk weather, not fasting on an exposed beach with hungry young to feed, but we appreciate the bounty of this coast almost as much.

•Accommodation was provided by Seaside Lodge, which has three-night self-catering breaks for four from £290